Kink decay in a parametrically drivenφ4chain

We consider the parametrically driven discrete ${\mathrm{\phi }}^4$ model with loss. Using an anaytical approach and direct numerical simulations, which turn out to be in excellent agreement, we demonstrate that there is a range of driving parameters such that kinks cannot exist in the system. This effect may be understood with the help of an averaged external potential energy of the system, which has no double-well structure in this region.